The project proposes a concept of piezoelectric adaptive thin shell reflector for future space telescopes; it exhibits excellent areal density and stowability, and thus, paves the way to future large aperture space telescopes. Controlling the surface figure of spherical or parabolic shell with in-plane stresses induced by a piezoelectric layer raises two problems:
(1) Doubly curved shells are significantly stiffer than flat plates and
(2) When using segmented electrodes with different voltages, the surface figure is subject to edge fluctuations.
This results in a very large number of electrodes, leading to ill-conditioning in the Jacobian matrix of the system; to solve this, a hierarchical approach is proposed to inverse the Jacobian, based on Saint-Venant’s principle. This research also provides a petal configuration design which aims at reducing the hoop stiffness and improving the foldability of the reflector.